// Decorrelation Stretch

function dcs(image, region, scale) {
  var bandNames = image.bandNames();

  // The axes are numbered, so to make the following code more
  // readable, give the axes names.
  var imageAxis = 0;
  var bandAxis = 1;

  // Compute the mean of each band in the region.
  var means = image.reduceRegion(ee.Reducer.mean(), region, scale);

  // Create a constant array image from the mean of each band.
  var meansArray = ee.Image(means.toArray());

  // Collapse the bands of the image into a 1D array per pixel,
  // with images along the first axis and bands along the second.
  var arrays = image.toArray();

  // Perform element-by-element subtraction, which centers the
  // distribution of each band within the region.
  var centered = arrays.subtract(meansArray);

  // Compute the covariance of the bands within the region.
  var covar = centered.reduceRegion({
    reducer: ee.Reducer.centeredCovariance(),
    geometry: region,
    scale: scale
  });

  // Get the 'array' result and cast to an array. Note this is a
  // single array, not one array per pixel, and represents the
  // band-to-band covariance within the region.
  var covarArray = ee.Array(covar.get('array'));

  // Perform an eigen analysis and slice apart the values and vectors.
  var eigens = covarArray.eigen();
  var eigenValues = eigens.slice(bandAxis, 0, 1);
  var eigenVectors = eigens.slice(bandAxis, 1);

  // Rotate by the eigenvectors, scale to a variance of 30, and rotate back.
  var i = ee.Array.identity(bandNames.length());
  var variance = eigenValues.sqrt().matrixToDiag();
  var scaled = i.multiply(30).divide(variance);
  var rotation = eigenVectors.transpose()
    .matrixMultiply(scaled)
    .matrixMultiply(eigenVectors);

  // Reshape the 1-D 'normalized' array, so we can left matrix multiply
  // with the rotation. This requires embedding it in 2-D space and
  // transposing.
  var transposed = centered.arrayRepeat(bandAxis, 1).arrayTranspose();

  // Convert rotated results to 3 RGB bands, and shift the mean to 127.
  return transposed.matrixMultiply(ee.Image(rotation))
    .arrayProject([bandAxis])
    .arrayFlatten([bandNames])
    .add(127).byte();
}

var image = ee.Image('MODIS/MCD43A4/MCD43A4_005_2002_07_04');

Map.setCenter(-52.09717, -7.03548, 7);

// View the original bland image.
var rgb = [0, 3, 2];
Map.addLayer(image.select(rgb), {min: -100, max: 2000}, 'Original Image');

// Stretch the values within an interesting region.
var region = ee.Geometry.Rectangle(-57.04651, -8.91823, -47.24121, -5.13531);
Map.addLayer(dcs(image, region, 1000).select(rgb), {}, 'DCS Image');

// Display the region in which covariance stats were computed.
Map.addLayer(ee.Image().paint(region, 0, 2), {}, 'Region');

